Talbot lasers are based on acousto-optic frequency-shifter (AOFS) loops seeded by a cw laser. When a single-frequency laser injects a frequency-shifting loop (FSL) system, constructive interferences occur periodically with time generating pulses at a repetition rate equal to (integer Talbot effect) or with a multiple of (fractional Talbot effect) the mode spacing of the comb. Talbot lasers have been shown to provide high-repetition rate pulse trains and have been applied to RF-optical signal processing, spectroscopy, and ranging. Here we investigate an all-fibered frequency-shifting loop (FSL) that includes an electro-optic intensity modulator (EOM) instead of the AOFS. Experimental results show that the intensity-modulating FSL generates short pulses with a repetition rate multiplication. It is based on the temporal fractional Talbot effect by adjusting the modulation frequency f_m and the fundamental frequency of the loop f_c as the ratio of two integers: f_m⁄f_c =p⁄q, leading to a repetition rate equal to qf_m= pf_c. In the experimental demonstration, the fundamental frequency of the loop f_c is constant while the modulating frequency f_m is adjusted thanks to the EOM. We observe pulses at a repetition rates tunable between 6 MHz and 600 MHz. The system is modeled by a simple linear interference model that takes the amplitude modulation function and loop delay into account. The model predicts the fractional Talbot property as in AOFS-based systems, but with an additional amplitude modulation of the pulse train, in good agreement with the experimental results. This experiment shows an alternative approach to AOFS loops, taking advantage of the inherent bandwidth and tunability of the EOM. This fractional Talbot laser may find applications in optical sampling, THz generation and ultrafast data processing systems.